An echo subtractor is one of the key components of an echo canceller. It also distinguishes it from a pure echo suppressor, that only attenuates the signal when echo is present. The main benefit of an echo canceller is improved performance in situations with simultaneous speech from both ends in the communication (so called double-talk) and also an increased transparency to low-level near-end sound, which increases the naturalness of the conversation.
Echo subtraction is usually implemented using a linear model, primarily because a linear model is computationally simple to estimate, but also because it is much harder to find an appropriate nonlinear model that works in general. For these reasons the echo subtraction generally cannot remove nonlinear echoes originating from nonlinearities in the echo path.
Another key component in an echo canceller is a residual echo suppressor, which reduces any residual echoes present in the output from the echo subtractor to such a level that the requirements on echo attenuation imposed by the relevant standards are fulfilled, and to such a level that the residual echo is not noticeable in the presence of the near-end signal. However, since the suppression performed by the residual echo suppressor also affects the desired near-end signal if the frequency content of the near-end signal and the residual echo are overlapping, the suppression performed by the residual echo suppressor should be as small as possible, as the transparency loss (of the near-end signal) introduced by this component is directly related to the amount of suppression performed.
Harmonic overtones in the loudspeaker output caused by nonlinearities will be picked up by the microphone as nonlinear echoes. These echoes also need to be removed by the echo canceller. However, as the echo subtractor is based on a linear model of the echo path, the echo subtractor cannot reduce the nonlinear echoes. These must therefore be removed by the residual echo suppressor. In order to do this the residual echo suppressor needs an estimate of the power of the nonlinear echoes. Furthermore, this estimate has to be accurate, since otherwise the residual echo suppressor needs to perform extra suppression (plan for a worst case scenario) in order to compensate for the uncertainty in the nonlinear echo power estimate. This will then result in reduced echo canceller transparency of the near-end signal, which is undesirable.
One class of methods [1-4] of modeling harmonic loudspeaker nonlinearities is based on a Volterra model using powers of the loudspeaker input signal. This is, however, computationally very complex. Furthermore, the harmonics produced by the Volterra model are typically aliased, so an up/down-sampling scheme is needed to avoid the aliasing to affect the power estimate of the harmonic loudspeaker nonlinearities, which makes the Volterra-based solution even more complex.